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Unformatted text preview: CHAPTER I s Enimdsetésn is Meeeis We now discuss modeiéng concepts so emphasize what is impomam in
buﬁding transposmtioa models. If we are thinking, for example, about
deveioping 2: sransportation mode} ofthe Boston metropolitan area, we
can reiatévely quickly come up with any number of modding issues
we wouid have to deal with in representing transportation in Boston. For example, we have so decide aeout {he scaie at which to stuciy
Bosion. How many nodes do we represent Boston wish? 5? 58*? 500?
5,000? How many iinks? At the link ievei, we have modeling choices:
do we represent trafﬁc as a set 05 individual vehicles (discrete meek-:3) or
as a ﬂow {eontinuoos modei}? A: the node levei, we can represens a
bus tennimi, for example, as a deierministic (Edgy function or we. can
model it as a eos‘nyiex microwsémulation, which gives us a proﬁabiiéstic
regiment-soon of delay for each veiséeie. Whaz are the impﬁcatiom of
these decisions? How many digerent modes do we consscier in éeveioping this
mode} ofBosion transportation? it is clear tint we would have separate
modes for automobiles and transit, but do we need a separase mode for
waEkess and bicyclists? Shouéd these modal mocieis 211% be insercon—n
neared? Or, should we have inciependeni: models representieg each of
these modes? $10an we consider the flows on the networks as smtéc, or
shouid we represent ﬂows dynamieaﬂywas a function of time? Shouid we consider short: run or tong mu issues? Do we aiiow
for changes is: laudnuse? Do we consider equﬁibsiom? We talk about
equﬁibrﬁum as a way to think about transportation systems, and we 211i
beiieve is; however, it is interesting how many models we come up
with the: are usefu} bu: ignore egoﬁibrﬁom. $36 MGﬁﬁLENS CONCEP?S Emmy, x 1.1
Hierarchy (ﬁrrlodds. ﬁlerarthies a? Moﬁels 5’). key nmdcling conccpt is that ofl'licmrchics 0fn-mcicls (see: Figure 11;):
Very of‘ecn we have modsls efcomponems {hat dcscrihe ihc blahavior 95
individual links or DGdCS. They desm’ilve how a trafﬁc intersectien or a
highway link perfbrms. We might have rclationsi‘zigs that describe ﬁew
fuel is consumtd anti haw emissions are produced by a vehicle as. a
ﬁmctﬁon of velocity and accclcmtéon. We have models that (icsmlxg
how customcrg cheese among trausportazion moécs laasecl (m Elnpiﬁgai
data. All ofthcse models {it together in some hierarchical way that gives
30:11:: broader represenmtion of a regicm iikc {ﬁe Boston area This might lead {0 models of cconemic growih, of landmusgl
of nciwork behavior, all of which are based cm l9w~levcl, more
detailed moclcls dealing with fuel consumption, vchicle emissigng,
link bahavior, 0: node ljchavior. Thoae dctailacl medcls ofcompgnem
bchavmr lead as $0 an apprapriam macroscopic medal of evemﬂ
systci'n behavior. ﬁﬁaﬁgﬁng¥ssues There are many modcling issues on which m focus. Through expe—
rlcncc, Wt: have learned ahat the fellowing issues are imperial: in
deciding how {:9 develop a sransportation model, gougejaries The ﬁrst issue is boundaries. Eran chi: ﬁeld of struczuml cuginceﬁng,
we have the concept of frembedy diagrams (see Figure E12}. We take
an claimant: and isolate: it from the rest of the structure; we analyze it by
representmg the entire rest of the. structure as a set of farms azlé
moments an that element~se it is a free boéyc Macroscopic madei
of aysiem behavmr Detailed models of
compeaené‘ behavier .EN'I‘EHJSJULL'I'aQN T0 TRANSPORTATION SYS‘rEMS Fist
ere ; Piazza
A com
when? lN'rR Kids (sec: Figurs: 11$),
scribe the behavior of
:43}: intersection 0; a
:ips that éescribe how
:ed by a which as a
medals that describe
less bascci or; empiricaé
rchicai way that gives
Eiosmn arm. gmwth, 0f haciwuse,
on Eowwicvei, mars
a, which? Emissions,
nodc‘is ofcemponsm
éc made} 0%" overaii acus. Thmagh expa—
165 are. important in :uctura} enginecﬁng,
ﬁgure 11.2). We take:
um; W5 analyza it by
a 565: if forces and maﬁa}
havéar ﬂTEO-N SYSTEMS INTRODUC‘I‘EON i?! a: 3‘ 3% Baum 1 2,; £5. {aye—{70d}! diagram.
% E; E. k. E 5: g E f E} E i i E g: E i g g Emma IL} 5: A rompiex syxtcmmm
E where £5 21w éowza‘aqt? Satmﬁucﬁon is: Maéeis ‘53? / We haw the 52:13:: isms m Eraszsporcation :‘ilodchng {scc Figure ”£1.30.
What are {ha limits we impose in smdying the system? Where (in we
draw the *boundasy? What is {putside anci win: is inside? An: we going £0
consider changes in technoiogy over €ime? Are we going to considar
changes in iamdmse? Are we gaing :9 congider whaﬁ our compatiiion
does, or is this maﬁa} intended {a teli us oniy what 1:0 do in the next two
h€>urs, and we. RSSEEITK‘: that our competition cannot (is aux/{hing in {bat
time frama? Are: we going t0 éook at econoimc impacts, environments}?
impacts, anﬁ grow‘ih of’m urban area? Macmsmgic Versus Micmsmgéc Madam Another modeling issue: is the levﬂ of demﬁ—macmsmpic versus 1mm
scopic models. For exampEe, as we mentioned, cadier. we can modai a A pessibie
system / boundary Operaiiuns . . ' Technaiogy
Companion AEE quaiiiy,
resourceés Land use Ewnemic
growth TO TRANSPQEITATION SYSTEMS iSS MQEELING CﬁNCEPTS temiinui as a Simpic L'it‘EL’l‘l'l'liiliSEiE.‘ (ﬁshy ﬁnictien or through a migm
scopic simuiuiimz. Siam Versus {Eyiiamie Mosﬁais We distinguish bcmreen static and dynamic i'iiOCit‘iSA—dt) we use 1210‘};ch
in which we assume the. kcy variabies are independent oftimc or {is Wt:
taik about tinic—depcndeiit ”width that ﬂy to reﬂcci‘ rushwhour pﬁgks‘
as apposed to steadywstate operations, in our study of {taxispormtimé
systems? Do we assus'iie static human hehavier {31" do we model we
reactions of peopie :13 situations; change? Staizhaﬁﬁc Vamus Qe’ierministic Moéais A fundariimtai qusstiozz is whstiicz' {0 represent transpoziation as a
stochastic or a deterministic system. We. have ciiscusseci S£0£hasticiiy as
a charaﬁeristic of transportation, but i: may wail {um out in some
applications rim wt? can gain some insighz 3:26 knowiedg€ 33y simpiy
reprcscsizing a system as detcmiinistic. Linear Versus ﬂaniénear Madam We taik about iinear varsus tmniiueaz‘ E‘ﬂpfﬁsel'iﬂﬁiﬁl‘lsi When we mlk
about using linear programming :9 menize a sysittim, Wt: are basicaiiy
assw'ning a iiiiear View ofthe world. it may be incerriici, but: iioniizicar
models, while more correct, may be much mere difficuit $9 501th Lin—
ear versus rmziiinear iimdcis is a gaod exampie ofthc trade—ogbctween
emistmciirag iiiodcis [i135 can preduce answers reiativciy easiiy versus
medals that mpmsmit the work} better but turn out to be more difficuit
{a solve. ﬂaminmus Versas DiSCieie Mmﬁeis We talk about cositiuuoais vsrsus :iiscmtc iizodﬁis, Speaking maﬁzeimtb
caiiy for 21 moment, WQ iconic? €31}: abom rcpréscnting the worid as a sei
of diﬁi‘rcntiai equatiens, that is, as continuous equaﬁons; or we can
rcpressnz the. W’Orid as a 36$ ofdifftrczict? equatieiis. ﬁt 5mm: point is} an?
iiws, we’ve. had some {zmciign tin: had to be intﬁgmtﬁd*—W£ iiiiii
to get tin: arm under tin: curve {mm X1 {0 X2, and for whatever reasoﬁ iNi‘EQi)U<‘:'¥EUN 1'0TRAN5POR'IATIQN SYSTEMS in '1 01” through a :13ch" :irw’ig we use medeig
dent chime or do We
ﬂeet rushwheur peaks,
13d}; of transportaiion
or do we modei the 1% transpcrmtéon as a
name? stochasticity as
fl'i {um oer in some
:zmwledge by simply 30:13. When we {aik
rem, We are basicaﬂy
ozrreez, but eoniénear
ifﬁcuit to soive. Lin~
1e trademeffbetween
iativeiy easiiy venue
: to be more diﬁkuit peaking nmtiwmatie
eg the world as 21 set
guetéons; or we can
kt some. point in our
megrated we had
far whatever reason ”mum Sve'rnms EzGUKe 11.4,
Grass representatim am!
derailed‘ representeﬁmz. [NTROEUC'i'EON inirecﬁuctioe ts: Mudets $39 the function was in web a farm that :10 matter how much we
looked through Our miﬁe ef‘imegrak, we could not ﬁnd the answer {see
Figure HA}. What we do in that: case is a numerical seluiion‘ We say, “Let’s
break this area up into rectaugies and let’s compute the area by adding
the rectangular areas." We recognize that the amount of mm: that we
wili have is a function. of haw many reciangies we have. if we have
a {aiziy grass representation, we may make a big mismke; if we ﬁave a
demﬂed representation, we can some up with a more accurate answer.
it is ihe question. between continuous amci discrete represenzatéom
0f reaiity {hat we are talking about here and how eéosely {he ﬁiscrege
representation reﬂects the continuous representaﬁen. The gross represeetation preduces quick answers-“mere are fewer
rectangles. The price you pay is accuracy. The detailed representazien
preduces a more accurate answer bui gakes more timema Ciasséc
modeling tméemoﬂ ifwe have a fainctéon y m {{x) that we can integrate in closed form,
the way :20 get: the area under the curve is m simpiy integrate. But, ifwe
have a function that we do not know haw £0 integrate (anti this is often
the case), we have to 3:39 tiimugh this in a linear fashion. Ifthe horizon-
taE axis is time, we are sieppmg {he model through time. TO T]{ANSPOR'£'A'}'E()N SYSTEMS 14G MOBELING GQRQEPYfi Heme 21.5 A
KimM;afi02?%$!{’ppfﬂg a
mode! Efamugh rims: Nemerieai Simuiatian Verges ﬁsasaa $9M! Seietiea These are numerica} or sinmiation analyses; they turn m1: to be yaw
1156*qu fbr generating results because we can Virtuaiiy aiways d0 3
zmmerieal er simulation analysis. Semetimee, however, {hey can be
very expensive because they take a leng time :0 {as}. An anaiytjcgg
closedmform i5 better if it preperly represents reality (see Figure 11.5} We can extené this hie-.1 to stochastic sysmme (icing prebabiiise
:ie simulatiom by using computer pregrams caﬁed randomwnumbe;
generators to represen: preeabﬁéstic heﬁavéoy in the system of interest, Eehaviemi Verses Aggmgate Moﬁais Agaether modeiing quesaen is beha‘vﬁoml versus aggregaie representatiom
We have discrezeweizoiee models foe modding what people tie in making
transportaﬁon and relateci choiceswowcalied behavioral medels, Aggregate representatiens are possible as weil. The ‘eesi: know:
example is probably the gravity mode; where we can mode} {he
amomzt of ﬂow bezween iwe geographic points as inversely prepay
{ions} to some functien ofthe dismnce betWeen {hem or, mom genes
aily, the resistance—wiismnce, quality 05 reads, and: so fereh. The
deveiopers of the gyavity mode} dtew 11pm: the insights of Newton
in the context of mechanicg; the idea is that perhaps Cities or regions
within areas weriz: that way as weﬂ. The ﬂow between them is inversely
preportiormi H) the square ef Ehe resistance {01" same other power)
iaetween chemhhence the name “gravity moeiei.” Beth behaviorai snzi
aggregate medels can be useful? for particaﬂar appﬁicaziens. §’hy$icai Verna Mathematicai Madam Another dissinc:£iox1 is between physieai and mathematicai modeis. In
some areas of syssems, we can physicaliy builci 3 mociei. in ﬂuid /‘v _ m} Time 3
Yime
Time
inputfuneiéone Ouiputfunciiens INTROIJUC‘i'iUN ‘E‘O TilﬁNSPOR‘i‘ATiON SYSTEMS ian turn out so be vary
rtually always (la a
wever, they can he
3 mn. An analytical
y {see Figure $1.5),
15 daing grobabiiis_
ed madam-number
2 system {sfimemss gate repsesematiens.
)eoggle do in rushing
ml models. . The best knGWn
NE: can model the
; inversely proper—
m ore more generm
and so forth. The
nights of Newmn
gs cities or regiesss
:h them is inversely
sme other power) {ash behavioral am}
ti<>rss. zestical models. in
: moéel. in ﬂuid M Time {st functéons lBN SYSTEMS iatroauction :9 Models 3&1 mechanics labs, we might ﬁnd wave masks; it is a physical scale repre—
seamtlon of reality am? we cuuici do experimems using it. Models of
structures are another good example. Salusien Yaehmaues Finally, we mention solution sechniques. Gating answers from the
model is fundaz'nemal ta what transportatian professianals do. We an:
often dealing Wish large~sca§e problems Where we are Optimizing
Complex systems, The brute force method of looking at every 9035i»
hiiéty is one of the question. Transpomtien pmfessionals have billions
and billions of Options, so coming up with some efﬁcient method far
mathematically seazehing through decisien 393% using optimization
theory is czﬁieah Sometimes? scaling dawn the problem to make it easier to solve is
an appropriate serategy when we develop models to predict perfonm
ance. As nosed earlier, deciding between simple sepsesentsilens using
closedwfosm mathematical solutions or complex sénmlation models to
generate answers is very i‘inpOﬁBFit. understanding she §ystem The key is kﬁewing whas‘ approximatiohs we can make in mpreset‘ztiz‘:g
reality, ané this is where an understanciing ofshe system, in om: case the
immsportatisn system, Games into play. We know what kinds ofsimplim
fications we can make and what khsds of models we need because
we uziderstand the transporsaeéon system and the kinds of questihns we
want answered. We are not interested in models per se (althozsgh
they are fascinatiag in and ofthemselves). We are interested in transporm
ﬁssion; models help us to make trasssportation systems heater. Now, many transpertation people make inspoﬁam modeling
advancesM—improvemenss in techniques—faster opgimizatiorz algo—
rithms, superior stasistieal analyses, and so ﬁmh. I {and others) have
observed that often those advances ase achieved by people with very
harcl spglications to comidermlike trazssportasian. To address ehese
applications, they end Lip advancing the state of the an: in modelihg. This is an imyorzam kind efaaivity. Many ﬁnd it diflﬁiculewimposw
sible, maybe—«t0 think about impmving modeling technique in the
abstractwahsent a speciﬁc prehlem. I believe {has many mocieling ENTﬁOﬁUCTEON TO TRANS?ORTA'{1GN SYSTEMS m MG§£LENG CGMEEPTS advances an: nude by $269916 with inmacmble appiications about Whig};
they need answegs. How {i0 wc decide which kinds ofmodeiing concepts to use? T0
answcr (his, we have go go back to wily we mode}. We nwdcﬂ m L:1)derswnd~~——msigh£ modeis; WC menial to axpiaéu; WC
model {0 pmdict; and we modal ti) inmmve. The ﬁmdammm} questien
we ask when ws arc: deciding what kjmi ofmedei {0 use is: WM: are we going {0 we the remlisjbr? Be the. msults; numericai or simply imights, haw are “WC“. going us:
£11059 rﬁsuhs? That shouid gavem the way in which we Cheese :0
modei. Efwc are going to talk about a mode} that is a matter oﬂife and
dﬁaih"—"ifthC? nmdel is wreng, the astronaut gets hiked—“We have wry
{iiﬁl’reni requirements for the modal than if WE an? sémpiy looking
at a modei as way cfdcvcbping a ﬁrswordcr undersmzzding efa transu
pm‘tatéon network. Rcmmnber: xﬁla.’ madcis am: wrong.
However, same are usg’fuf. Ali models are abstractions {113% diminata some rataiity. "131:: acid
asst is whedxsr the zalociei pmduccs results that are uscﬁli in cm: areas of
émcrest. Transparimimz sys‘femx are mmgiax, dynalm's, am? {mermxiiy im‘ercmmected {15 we?! as {ﬂier/(amazed wiﬂs other campiex
aiyrrcirriia: systems (9.3, the cz-szxiros-zmer—II) {he awrwmy). N16}! vary in space) and firms (mt dgﬁiérsm {in-m scaiérsjér dfﬁérerif componemﬂ
Serm're is pmyia’eci m cmnpiex nezzyories. W58 systems are smdmﬁzéc in mime. Human darn'5iot1—rzmkerg whiz somyiex décisiarz {afcrdzk
make (from; Igza? shape {he trmispormrfiozz 5313mm. INTROSUCTIUN TC) TRANSPQR'I‘A’I'IGN Sys*;*1ams IN‘E‘RQ cations about wind} :anepts to use? T3 Mic? to cxpiztin; we
miammata} questien
:0 use is: :r? v are: we going use
ich we choose to
a matter ofiife and
{:6 we. have very
n: simpiy looking
tanding of a transw rcaiity. The acid
:2qu in our area 0f -’ furmzaify
' «rompz’ex Norway}. went wr-npwzeuis).
éockasti: :‘n fiafzii’a’i. mics/134i
mm. um SYSTEMS issues in Mﬁdei Suihﬁﬁg 343 J‘s/{adding 5hr: 5mm 5}»st £3 czﬁnwst iricwmivaiza’e. Ow {tlmﬂeizge is m (110059
Wigwam sziésysfems (md made! mm appmpricztefyfor the intended purpose,
mimg‘hli}; reﬂectirag {he boundary egfﬁrefs afﬁx: ammodeiad companmrs. Ifwe are considering at a made}. to use in real time we are actualiy
going to comm} the real system in real t.éme—~we have. to think abmzt
sch/Ting the model fast anoggh {0: ii to he: useful. If we am going use ﬂu»: modei for sensitivity anaiyses~ acid six
trucks to the ﬂeet and pmdict ievei—oﬁsewice change—{£16.11 we have
:0 {kink abeut those sensitivity analysas as we buﬂé the model. We
have t0 mink about ﬁat: knobs WE want; ti) turn on the nmdci when we
build the 2110661. if we are inmrested in opiimizmg the graft}: Eight
gaming in 303mm? we berm; not represent the wheie Boston tmfﬁc
Eight grid as; a single aggregate delay function. We. Wiﬂ not get very far
with that kind of {epmgenizatéon if wizat we med is :1 microscopic
rcprcgentaiiim of individuai intersections, isms ii? magi Bu‘éisﬁiag iN’raobucz‘ION There an: somc pragmatic issues we deal mm in modci baéldéng. is the
mociei the right one? is it “true?” We paraphrase john Dfswey on
the topic of how we know a moéei is “true.” Our modei @055 no: work in practice immme it i5 Hue; mike; we hold our
model in be? true because? it works in, practice. “me and Reswmes Wa 1mm worry about tiny: and researces -------- money? computers, and
peopie. When {has the: 33055 want the answer? What is our budget? Betta We have to think about data. What data dz) we have? What is avaiiablc
t0 caﬁbiase {his mode} to ensure that it“ is operating correctly? How
axpensive is it to colieca more? Data is aimost always 3 major considcmm Lion in real~wodd transportation systems. ‘I'U TRANSPORTATEON SYSTEMS 341$ MDQEZLENQ CGNCEPTS Designing a Suctessfui 3%}ng We ail Want m be successﬁli: how do ‘WL’ design a made! that is $9ng
to be succcssful? By successful, we mean uscﬁﬁ and uscdm-at 50mm
isveiwby the decisionmz'nakcrs for whem we designcd and 1111;316—
mentcd it. SL3CC€SS in modeling i5 more at: art than a science. Here are
some ways cf measuring guccess. Ease of Use The tactical ofcase ofme, dcvcigping uscrmfmcxzdly modcig is impormm
ﬂcvcloping medals that providc resuits in a farm that is consistent With
the way it: which organizatiens make decisions is very important If
{hrs kinds ofoutputs our made} is producing arc in some way dchrgem
from the way in whicéz thc viccupresidcnt ofopcrat‘ions wants to make
{icciséons about how she runs the network, the 3110ch is not going to
£35 used. Coméméng Metﬁais Buﬁdiag mode-:15; that arc convincing, that make intuitive sense to the
user, is important. 6:1)th Pam Proviciing .s'noticis with a growth path that: we can modify or cxpazlé
over time as Situations chaagc is impm‘tzmt t0 lengmtemi success. iﬁmduce Beneﬁts Having medals that produce beacﬁts is ﬁmciamcmal; we want to be 3:918
to say, “i uscd this moéci and now {he META was better.” To haw
that outcome Ciﬁit‘r through the insights that management: gained 0:
though dircct rcsuits that managenmnt was able: to use—“cozm’ng up
wiih benefits-miss very important. Success breeds succe35wdevcioping a
track record of useful reguits and demonstrabic beneﬁts is important, Mmsuring Moﬁei Success The ways in which people in pmctécc and {huge in academia measzuﬁ
this: success of models may (ﬁffar substantially. its a researcher, when i INTRODUCTION ":9 TRANSPGETAIION SYSTEMS New ﬁevelepments Er: Moéels and Frameworks 1135 look at a model, i {look about concepts like unique solutions and
assuring tho: there is a strong rheoretical base. However, when we go out to practice, geopie ask: “Does it help
me in myjoh? Does it make me be a better vicempreséeleor ofMarkering
than I was before i had this model?” in a some the notion is, “l Clo not
care ifyou use a Ouija Board to get me these results; l do not really care
about {he underlying basis ofrhis. I just wan: to Clo a beteerjo‘o.” There
is a tension there berweeo {he perspeetives of rhe academic researcher
and {he oerspectéves of eeople actually using morsels in the ﬁeld.
Sometimes the difference in priorirles leaés to some academic models
not heing as useful in gracrlce as $1153; mighs: be. There are two ways that: we advance in rranspormtion. One is by
advancing modeling merhoclologies—w—by thinking about: how :0 make
better models for trans...
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